Branes with fluxes wrapped on spheres

Following an eight-dimensional gauged supergravity approach we construct themost general solution describing D6-branes wrapped on a Kahler four-cycle takento be the product of two spheres of different radii. Our solution interpolatesbetween a Calabi-Yau four-fold and the spaces S^2xS^2xS^2xR^2 or S^2xS^2xR^4,depending on generic choices for the parameters. Then we turn on a backgroundfour-form field strength, corresponding to D2-branes, and show explicitly howour solution is deformed. For a particular choice of parameters it represents aflow from a Calabi-Yau four-fold times the three-dimensional Minkowskispace-time in the ultraviolet, to the space-time AdS_4xQ^{1,1,1} in theinfrared. In general, the solution in the infrared has a singularity whichwithin type-IIA supergravity corresponds to the near horizon geometry of thesolution for the D2-D6 system. Finally, we uncover the relation with work donein the eighties on Freund-Rubin type compactifications.Comment: 15 pages, Late